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Expressions for neutrino oscillations contain a high degree of symmetry, but typical forms for the oscillation probabilities mask these symmetries. We elucidate the $2^7=128$ symmetries of the vacuum parameters and draw connections to the choice of definitions of the parameters as well as interesting degeneracies. We also show that in the presence of matter an additional set of $2^7=128$ symmetries exist of the matter parameters for a total of $2^{14}=16,384$ symmetries of the vacuum and/or matter parameters in the oscillation probabilities in matter. Due to the complexity of the exact expressions for neutrino oscillations in matter, we show that under certain assumptions, approximate expressions have at most $2^6=64$ additional symmetries of the matter parameters for a total of $2^{13}=8,192$ symmetries. We investigate which of these symmetries apply to numerous approximate expressions in the literature and show that a more careful consideration of symmetries improves the precision of approximations.
In a previous paper, the author proposed Symmetry Finder (SF) method for hunting symmetries in neutrino oscillation in matter, which essentially identifies a symmetry in the diagonalized Hamiltonian in matter. It was successfully applied to Denton {i
Three-flavor neutrino oscillations in matter can be described by three effective neutrino masses $widetilde{m}^{}_i$ (for $i = 1, 2, 3$) and the effective mixing matrix $V^{}_{alpha i}$ (for $alpha = e, mu, tau$ and $i = 1, 2, 3$). When the matter pa
We comment on the paper On application of the time-energy uncertainty relation to Mossbauer neutrino experiments (see arXiv: 0803.1424) in which our paper Time-energy uncertainty relations for neutrino oscillation and Mossbauer neutrino experiment (s
We study neutrino oscillations in a medium of dark matter which generalizes the standard matter effect. A general formula is derived to describe the effect of various mediums and their mediators to neutrinos. Neutrinos and anti-neutrinos receive oppo
Following similar approaches in the past, the Schrodinger equation for three neutrino propagation in matter of constant density is solved analytically by two successive diagonalizations of 2x2 matrices. The final result for the oscillation probabilit